Determine the order of the differential equation d^2y/dx^2 + xdy/dx + 4 = 0 (a)

Question

Determine the order of the differential equation d^2y/dx^2 + xdy/dx + 4 = 0 (a) First order (b) Second order (c) Third order Which of the following equations is a separable Differential equation (a) y' - e^y = e^x+y (b) (x+y)y' = x - y (c) y' = In(xy) (d) y^2 dx + (2x - 3y)dy = 0 An integrating factor mu(x) for the linear differential equation dy/dx + 5y = e^x is (a) e^5x (b) x^5 (c) -e^5x (d) 1/x^5 The solution of differential equation y' = 3x is (a) x^3 + Cx + C_0 (b) x^2/2 + Cx + C_0 (c) x^3 + Cx^2/2 + C+_0 (d) None A particular solution for the differential equation y" + 2y' + y = 3-2 sin x is (a) y_p = A + B sin x (b) y_p = Ax + B sin x (c) y_p = A + B sin x + C cos x (d) y_p = A + Bx sin x + Cx cos x

Explanation / Answer

1. The number of higest derivative in a differential equation is called degree. The highest degree in the given differential equation is 2. hence order of the differential equation is 2

b) is the correct option.

2.

From the given options we can separate variable in the first option only. Hence a is the correct option.

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